PLSC30500, Fall 2024

Part 0. Introduction

Andy Eggers

Welcome!

This course

  • Instructor: Andy Eggers
  • Teaching assistant: John Kainer
  • part of a sequence:
    • Intro to Quant Soc Sci (this course) (fall)
    • Causal Inference (winter)
    • Linear Models (spring)

Our objectives

  • give a strong foundation for further study
  • give a taste of what is fun about quantitative social science
    • mathematical rigor and clarity
    • thinking about estimation, uncertainty, causality
    • working with data (a little)

Broad plan

Five modules:

  • Probability (1.1, 1.2, 2.1, 2.2)
  • Summarizing distributions (3.1, 3.2, 4.1, 4.2)
  • Estimation (5.1, 5.2, 6.1)
  • Inference (6.2, 7.1, 7.2)
  • Regression (8.1, 8.2, 9.1, 9.2)

Expectations about background

Required to have some recent exposure to probability and R.

Useful (not required) to have exposure to

  • other math (semi-recently)
  • other programming
  • statistics
  • econometrics/regression modeling

If you have don’t have much exposure to \(X\), you may have to work harder on \(X\).

If you have lots of exposure to all of the above, we believe you can still learn something.

Expectations for the course

  • Read the syllabus (link from Canvas page and Github)
  • Prepare for class: attempt the main reading (Aronow & Miller); ask for easier readings if necessary
  • If you are stuck on reading/assignments:
    1. Use google first, or e.g. ChatGPT
    2. Ask your question on our private StackOverflow (https://stackoverflowteams.com/c/uchicagopolmeth)
    3. Or if you’re brave, ask on the real StackOverflow (https://stackoverflow.com/) if it’s about R or CrossValidated (https://stats.stackexchange.com/) if it’s about stats.
  • If you are confused in class, ask a question

Please also answer questions on our private StackOverflow.

If you email me a question, I am likely to tell you to put it on our StackOverflow.

Labs

Taught by John, Fridays, two sessions

  • 10:30-11:20 (Cobb 430)
  • 12:30-1:20 (SSRB 107)

Assessment

  • 40% problem sets (8 in all)
  • 10% class participation
  • 20% in-class midterm, session 4.2 (October 23)
  • 30% final take-home exam due December 10

Websites

All slides and assignments will be distributed via the course Github:

https://github.com/UChicago-pol-methods/IntroQSS-F24

  1. Download files one by one, or
  2. git clone and periodically update via git pull.

Homework submission via Canvas page.

Technical setup

By lab on Friday (ideally sooner), make sure you have R/RStudio installed, and can compile a qmd file to pdf.

  1. install R from https://cran.rstudio.com/
  2. Install RStudio from https://www.rstudio.com/products/rstudio/download/
  3. In RStudio install tidyverse and tinytex
  4. New file -> Quarto document; then Render to make pdf.

Motivation

What most applied social scientists “know” about statistics

Our goal in this class is to understand topics every social scientist needs to know:

  • Linear regression (OLS)
  • Statistical inference (standard errors, p-values, null hypothesis)

Many social scientists only know this, and most have important misunderstandings.

What most applied social scientists “know” about linear regression (OLS)

  • We use regression (ordinary least squares, OLS) to measure relationships between a dependent variable (DV, left-hand-side (LHS) variable, outcome variable) \(Y\) and independent variables (right-hand-side (RHS) variables, covariates, predictors) \(X_1\), \(X_2\), \(X_3\), etc: e.g. \(Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \ldots\)
  • We call the estimated “effect” of each variable a regression coefficient
  • For regression to work, you need a lot of assumptions, e.g. relationships have to be linear, the error term (or the dependent variable) needs to be normally distributed
  • A regression coefficient for \(X_1\) measures how much \(Y\) is predicted to change with a one-unit increase in \(X_1\), holding fixed \(X_2\), \(X_3\), etc
  • Sometimes this coefficient is a good estimate of the (causal) effect of \(X_1\) on \(Y\), i.e. what would happen if you changed \(X_1\)
  • You can use an interaction term to get a coefficient that measures how the “effect” of \(X_1\) depends on the value of \(X_2\): \(Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_1 \times X_2 + \ldots\)

A regression table

What most applied social scientists “know” about other estimation techniques

  • When the dependent variable is binary (i.e. only 0 or 1), you shouldn’t use OLS
  • Instead you should use logit or probit
  • Logit and probit coefficients are hard to understand

What most applied social scientists “know” about statistical inference

  • Statistical software gives you a standard error for each regression coefficient. A bigger standard error means we are more uncertain what that coefficient really is.
  • The null hypothesis is usually the claim that there is no relationship. We do hypothesis testing to see if we can reject the null hypothesis.
  • If the p-value on your coefficient is below .05, your coefficient is statistically significant and you can reject the null hypothesis. This means the coefficient probably isn’t zero because the relationship is unlikely to have occurred by chance. If you get a p-value above .05, you didn’t find anything and your analysis didn’t work.

What we want you to know

You need to know the correct parts above! (e.g. reading regression table, interpreting interaction terms)

But also, we want you

  • to avoid the misconceptions (the stuff in orange and red)
  • to understand common approaches to uncertainty (e.g. standard errors) and hypothesis testing (e.g. p-values): the logic behind these approaches and their limits.
  • to see what coin flips and urns have to do with social science.